Optimal control of non-instantaneous impulsive second-order stochastic McKean–Vlasov evolution system with Clarke subdifferential

Abstract

Abstract The optimal control of non-instantaneous impulsive second-order stochastic McKean–Vlasov evolution system with Clarke subdifferential and mixed fractional Brownian motion is investigated in this article. The deterministic nonlinear second-order controlled partial differential system is enriched with stochastic perturbations, non-instantaneous impulses, and Clarke subdifferential. In particular, the nonlinearities in the system that rely on the state of the solution are allowed to rely on the corresponding probability distribution of the state. The solvability of the considered system is discussed with the help of stochastic analysis, multivalued analysis, and multivalued fixed point theorem. Further, the existence of optimal control is established with the aid of Balder’s theorem. Finally, an example is provided to illustrate the developed theory.